Research Progress on Radial Forging Process of Superalloy Alloy

High-temperature alloys, as critical materials for high-temperature components such as turbine blades, combustion chambers, and turbine disks, are widely used in aviation, aerospace, and energy sectors due to their exceptional performance under extreme temperatures. However, controlling the microstructure of these alloys remains a significant challenge in practical production. Radial forging technology demonstrates remarkable potential in high-temperature alloy manufacturing, offering advantages like high efficiency, material utilization rates, and significant improvements in forging microstructure. Through multi-head hammering and high-frequency forging, radial forging achieves uniform deformation of raw materials, enhancing both mechanical properties and internal density of the forgings. This study systematically examines the driving principles of radial forging equipment and the impact of key process parameters on production processes. It analyzes the microstructural evolution mechanisms and grain growth patterns of high-temperature alloys under multi-pass high-frequency forging, compares the applicability of different forging penetration models, and summarizes current research progress on stress-strain constitutive models and microstructural evolution models in finite element simulations. The study highlights that high-precision multi-physics coupled simulations and intelligent process design represent core future development directions.

1 Introduction

In modern manufacturing, superalloys are extensively utilized in critical industries such as aviation, aerospace, energy, and automotive sectors due to their exceptional high-temperature resistance and corrosion resistance. These applications impose stringent material performance requirements, particularly under extreme operating conditions. In practical production processes, precise control of the microstructure of superalloy bars remains highly challenging. For instance, during forging operations, the precipitation amount, morphology, and distribution of δ-phase in GH4169 alloy are difficult to regulate, which significantly impacts the material's mechanical properties at elevated temperatures. GH4720Li alloy often develops surface cracks and coarse grain layers during forging bar formation. Additionally, GH4037 alloy bars exhibit uneven rolling-state microstructures, frequently resulting in coarse grain morphology on the surface that causes excessive noise levels during flaw detection. Therefore, developing effective processing techniques to optimize the microstructure and mechanical properties of superalloys remains a pivotal research focus in materials science and manufacturing technology.

Radial forging, as an advanced metal forming technology, has attracted widespread attention in the industry due to its high efficiency, high material utilization rate, and significant improvement in the microstructure of forgings. Originating in 1950, radial forging is a unique forging technique. During the forging process, multiple pairs of symmetrically arranged hammers perform high-frequency radial striking on the blank. Regardless of whether the blank is square or circular, it rotates and moves axially under the clamping of a robotic arm, resulting in axial elongation through the spiral deformation caused by multiple hammers. The machinery used for radial forging processes is called a precision forging machine, internationally referred to as a radial forging machine. Radial forging machines integrate multiple technologies such as hydraulic transmission, microelectronics, automatic control, network communication, and sensor testing, making them advanced equipment with minimal or no cutting processes. Currently, major global manufacturers of radial forging machines include Austrian GFM and German SMS. Radial forging machines in China are mostly imported from abroad; for example, Jiuli Group has introduced an SMS 18MN hydraulic radial forging machine. Recently, China's Lanshi Group has successfully developed a 1.6 MN mechanical radial forging machine and established a fully automated rod radial forging production line covering heating, forging, and straightening processes.

High-temperature alloy bars are currently manufactured through rapid forging, radial forging, or a combined "rapid + radial forging" process. Free forging involves outward deformation from the core of the billet, resulting in low final forging temperatures and severe cold deformation structures on the surface. Additionally, significant small deformation zones appear at the billet's outer edges, leading to inferior surface quality and dimensional accuracy. Radial forging, which deforms the billet from the outer edge toward the core, significantly improves surface quality. Furthermore, radial forging machines operate at higher hammering frequencies (with minimum hammering cycles twice those of rapid forging hydraulic presses per minute). The heat generated during deformation sufficiently compensates for heat loss to the environment, maintaining stable processing temperatures comparable to constant-temperature forging. This makes radial forging particularly suitable for forging high-temperature alloys within narrow heat treatment temperature ranges.

Although radial forging technology has achieved significant progress in experimental studies and small-scale production, it still faces numerous challenges in industrial applications, such as high equipment costs and complex process parameter control. This paper aims to review the characteristics of radial forging processes, as well as the microstructural changes and forgeability analysis of superalloys during radial forging. The study focuses on analyzing existing issues in superalloy radial forging processes and proposes actionable solutions, providing scientific guidance and technical references for optimizing radial forging techniques for superalloys.

Introduction to Two Radial Forging Processes

Figure 1a demonstrates a radial forging device featuring high-frequency pulse forging and multi-directional die forging characteristics. The high-frequency pulse forging technique enables smaller deformation per stroke, resulting in lower metal deformation rates, shorter metal flow distances, reduced friction forces, and more uniform deformation patterns (Figure 1b). By utilizing up to eight hammers to perform radial forging on the blank, the material is subjected to triaxial stress conditions that enhance metal plasticity. Consequently, forgings produced through radial forging processes exhibit excellent mechanical properties, dense internal microstructures, superior tensile strength, and impact toughness, making them highly suitable for manufacturing high-temperature alloy components.

 

2.1 Characteristics of radial forging

Radial forging can be classified into three types based on the temperature of the blank: hot radial forging, cold radial forging, and warm radial forging. These correspond to forging methods where the blank temperature is above the complete recrystallization temperature, room temperature, and above room temperature but below the complete recrystallization temperature, respectively. Hot radial forging is a commonly used radial forging method for forming high-alloy alloy bars.

2.1.1 Radial Forging Process Parameters

The key process parameters affecting radial forging include rotation angle, axial feed rate, forging frequency, radial reduction, and forging temperature.

(1) Rotation Angle: During radial forging, the workpiece rotates with the clamping end's movement, making the rotation angle equivalent to the clamping end's angular displacement. Each hammer stroke causes the workpiece to rotate through a specific angle, resulting in polygonal profiles on the outer edges of the forged bars. The polygonal edge count is directly influenced by the forging rotation angle rather than the workpiece diameter. Increased edge counts lead to more rounded shapes. When maintaining a fixed number of forging passes on a radial forging machine, the clamping end's rotation angle can be adjusted. When selecting rotation angles, higher angles and greater axial feed rates should be prioritized to enhance production efficiency while ensuring product surface quality.

(2) Axial feed rate: Defined as the axial displacement of the chuck per unit time. While increasing axial feed rate can enhance productivity, it reduces forging passes during the process, potentially leading to compromised surface quality of the forgings. Elevated axial feed rates expand the plastic deformation zone, which not only increases equipment load but also raises forging temperatures.

(3) Striking frequency: Striking frequency refers to the number of hammer strikes per unit time on the forging, typically expressed in strikes per minute. In radial forging processes, striking frequency is a critical parameter that directly impacts production efficiency, forging quality, and equipment load. Standard radial forging machines typically operate at striking frequencies ranging from 80 to 240 r/min. For high-temperature alloy forgings, the frequency is generally kept lower at 80–120 r/min to ensure optimal forging quality.

(4) Radial reduction: Radial reduction refers to the decrease in radial dimensions of a forging during a single forging cycle. Within the equipment's operational range, it is advisable to maximize radial reduction to enhance forging penetrability and improve production efficiency. However, excessive radial reduction combined with excessive axial feed may result in spiral wrinkles on the forging surface. Therefore, appropriate radial reduction should be controlled based on process parameters such as axial feed rate and rotation angle.

(5) Forging Temperature: Forging temperature directly influences the initial grain size of the billet, which in turn affects the microstructural evolution of forgings during forging. In radial forging, heat loss primarily occurs through heat exchange between the billet and external environment, as well as between the billet and the forging hammer. Due to the short forging duration and brief contact time between the hammer and forgings, the temperature drop is minimal. However, high-speed forging can lead to significant temperature increases in the core region of forgings. Research on radial forging of GH4169 alloy bars demonstrates that grain size is primarily determined by initial forging temperature, while the morphology and quantity of δ-phase precipitation are influenced by final forging temperature. These factors ultimately determine the microstructure and mechanical properties of the finished bars.

2.1.2 Radial Forging Process Parameters

Radial forging equipment typically features two or four hammer heads. While two-hammer radial forging machines closely resemble conventional fast forging machines in their dual hammer configuration, they demonstrate significantly higher reduction rates compared to traditional fast forging systems. As illustrated in Figure 2a, dual-hammer radial forging machines can be modified to accommodate four hammer heads. The hammer heads are mounted on rocker arms driven by a single drive shaft via eccentric cams. After workpiece deformation, the hammer heads return to their original positions through spring mechanisms. Adjusting the threaded bushings enables precise control over hammer spacing and axial workpiece feed rates. The intense hammer impacts generate substantial internal heat, necessitating water cooling systems to prevent overheating. Generally, four-hammer radial forging machines are more widely adopted than their two-hammer counterparts, as shown in Figure 2b. A key advantage of four-hammer systems lies in their ability to produce both square and round workpieces in a single pass, whereas two-hammer machines typically require multiple passes. Overall, four-hammer forging equipment represents a more complex and cost-intensive solution compared to two-hammer configurations.

Radial forging equipment can be classified into three main types based on drive mechanisms: mechanical drive, hydraulic drive, and hybrid mechanical-hydraulic drive (Figure 2). In mechanical drive hammer systems, an eccentric shaft drives a slider mechanism to convert rotational motion into linear motion, while a worm gear assembly transmits this movement to the hammer head. To ensure synchronized hammer operation, a gear system drives four eccentric shafts, enabling precise positioning adjustments through four worm gear pairs to accommodate various workpiece geometries, as illustrated in Figure 2c. GFM's SX series and SKK series radial forging machines exemplify this technology. Figure 2d demonstrates hydraulic drive principles: hydraulic cylinders propel pistons to drive hammer rods, creating reciprocating hammer motion. Fully hydraulic radial forging machines differ from mechanical systems by automatically adjusting forging speed and strike frequency based on hammer pressure and load conditions. This capability is particularly crucial for high-temperature alloy materials due to significant thermal expansion during deformation. By precisely controlling deformation rates and frequencies, operators can prevent overheating or excessive cooling while maintaining optimal temperature ranges. In hydraulic drive systems, direct connections between hammer heads and molds enable precise deformation control. Representative models include SMS Meer's SMX series and SMI series radial forging machines.

Figure 2e illustrates a hammer head device driven by a hydraulic-mechanical hybrid system. Four eccentric shafts mounted on an octagonal frame serve as the primary power source for the hammer head, driven by a synchronous gear system within the forging chamber. The hammer head's stroke position is controlled by adjusting the volume of hydraulic pads connected to the eccentric shafts. These hydraulic pads not only regulate stroke positioning but also provide overload protection and enable real-time monitoring of forging forces. The compact design of the hydraulic pads allows for highly space-efficient structural configuration of the forging machine. The forging frequency of this equipment is determined by the eccentric shaft drive system. A representative example of such equipment is the RF series radial forging machine developed by GFM Company.

3Evolution of Microstructure in Radial Forging Process

3.1 Processing Hardening and Recovery

Work hardening and recovery are two critical processes associated with grain structure changes during warm forging. Work hardening occurs during forging deformation, primarily manifested as increased material deformation, enhanced strength, and reduced plasticity. The rise in dislocation density within materials serves as a key factor in work hardening. During plastic deformation, dislocations continuously accumulate and interweave, ultimately forming dense dislocation structures (dislocation walls). These dislocations gradually evolve into compact dislocation networks through dislocation multiplication mechanisms, resulting in significant strength improvement. Under normal conditions, typical dislocation densities range around 10^11 m^−2, but increase substantially to approximately 10^16 m^−2 after deformation processing. Recovery and recrystallization processes are pivotal factors influencing forging microstructures, both of which are influenced by work hardening. During metal deformation, partial deformation energy is absorbed, leading to elevated internal energy and increased structural defects. When materials are reheated, they undergo recovery processes that reduce dislocation density, thereby forming more stable lattice structures.

Temperature intervals are classified using the reduced temperature TH=T/Tm (where T represents material temperature and Tm is melting point), primarily divided into three zones: 0.1<TH<0.3 constitutes the low-temperature recovery zone, during which point defects rapidly propagate and dissipate; 0.3<TH<0.5 marks the intermediate-temperature recovery zone, where increased atomic mobility facilitates dislocation slip or cross-slip, leading to subgrain structure formation and reduced dislocation density; TH>0.5 defines the high-temperature recovery zone, where sustained atomic activity enables dislocation climb and polygonalization processes.

The extent of material recovery is correlated with strain, temperature, and time, typically increasing with deformation magnitude, temperature elevation, and duration. Recovery behavior also depends on stacking fault energy—the intrinsic energy required for dislocation formation. Dislocation slip, climb, and cross-slip processes are hindered by stacking faults, thereby impeding recovery. Materials with lower stacking fault energy (e.g., nickel-based superalloys) exhibit more pronounced recovery tendencies, whereas higher energy barriers result in reduced recovery efficiency, increased dislocation density, and consequently fewer subgrain structures.

3.2 Recrystallization

During hot deformation processes, superalloys primarily rely on recrystallization mechanisms to achieve grain refinement. When the accumulated dislocation density in the alloy reaches a critical threshold during plastic deformation, fine recrystallization cores without obvious defects form within deformed grains. Under appropriate thermal deformation conditions, these cores can absorb surrounding deformed grains and gradually grow, thereby promoting grain refinement. Recrystallization behaviors mainly include dynamic recrystallization (DRX), subdynamic recrystallization (MDRX), and static recrystallization (SRX). Notably, MDRX and SRX are also referred to as post-dynamic recrystallization.

Dynamic recrystallization (DRX) refers to the recrystallization phenomenon occurring during thermal deformation processes, which plays a crucial role in grain refinement during radial forging. The dynamic recrystallization process involves two stages: nucleation and subsequent growth. The formation of new grains leads to material grain refinement, thereby enhancing the overall mechanical properties of components. According to our research group's findings, the dynamic recrystallization morphology of GH4169 is illustrated in Figure 3. Based on different formation mechanisms, DRX can be classified into three types: discontinuous dynamic recrystallization (DDRX), continuous dynamic recrystallization (CDRX), and geometric dynamic recrystallization (GDRX), as shown in Figure 4. In nickel-based superalloys, the DRX mechanism predominates, with CDRX playing a secondary role. However, some researchers have observed that these three types of dynamic recrystallization may not exhibit strict demarcation lines and could potentially occur simultaneously.

 

In 1950, Beck and colleagues first observed discontinuous dynamic recrystallization. During material deformation, grains exhibit varying deformation magnitudes. Those with greater deformation accumulate higher internal energy reserves, while less-deformed grains store lower energy. To reduce internal deformation energy, grain boundaries migrate from low-energy grains to high-energy ones, thereby lowering material energy. Discontinuous dynamic recrystallization primarily initiates through grain boundary protrusion. During boundary migration, dislocation density in traversed regions becomes zero. When nucleation conditions are met, recrystallization nucleates in these areas, forming necklace-like structures in metallographic microstructures. This phenomenon demonstrates easily observable growth processes. Unless otherwise specified, the term "dynamic recrystallization" typically refers to discontinuous dynamic recrystallization—the most extensively studied form. Azarbarmas' research revealed that in GH4169 alloy, recrystallization mechanisms differ by temperature and strain rate: CDRX dominates at low temperatures and high strain rates, while DDRX becomes the primary mechanism under high temperatures and low strain rates.

Continuous dynamic recrystallization primarily occurs in high-temperature alloys with significant deformation and high internal dislocation energies, particularly at trihedral grain boundaries exhibiting high dislocation densities. This process mainly involves nucleation and growth through subgrain coalescence, as illustrated in Figure 5. Under external forces, subgrain boundaries initially form within grain boundaries. As dislocations accumulate, these subgrain boundaries absorb them, leading to increased subgrain boundary angles. Eventually, these subgrain boundaries transform into large-angle grain boundaries, resulting in recrystallized grains. The transformation process reduces internal deformation energy and dislocation density while forming uniformly distributed fine recrystallized structures that enhance material properties. Zhang et al. found that CDRX tends to occur under low strain and low deformation temperatures. Lin et al. suggested that CDRX occurs under moderate strain conditions and is also prone to occur at lower temperatures.

The geometric dynamic recrystallization phenomenon is also associated with the transformation of subgrain boundaries and subgrain structures. Its key distinction from DDRX lies in its occurrence under extreme deformation conditions. In such scenarios, grains undergo significant deformation in a specific direction. As deformation increases, existing grain boundaries progressively converge while subgrain structures remain largely unchanged. With continued deformation, collisions and mergers of original grain boundaries lead to subgrain structure transformation into new grains, ultimately resulting in recrystallization phenomena.

During post-deformation multi-stage heat treatment processes, material microstructures undergo further evolution characterized by post-dynamic recrystallization, as illustrated in Figure 6. MDRX (Microdeformation-induced Recrystallization) occurs when recrystallization nuclei generated during DRX (Dynamic Recrystallization) fail to grow post-deformation. If the material temperature remains below the critical threshold, these nuclei will directly initiate growth, resulting in highly deformed lamellar grain structures. SRX (Static Recrystallization) phenomenon emerges when the material's deformation strain remains below this critical threshold, but post-deformation energy accumulation becomes sufficient to initiate recrystallization under heating conditions. Figure 7 demonstrates a schematic representation of static recrystallization microstructures.

Subdynamic recrystallization plays a crucial role during material deformation, significantly influencing microstructural properties. However, since it requires no incubation time and involves complex strain rate control mechanisms, its effects are often intertwined with dynamic recrystallization processes. Consequently, its independent impact is typically overlooked in structural analysis studies. In contrast, static recrystallization requires specific incubation periods. Post-static recrystallization grain size exhibits strong correlations with deformation parameters including strain magnitude, strain rate, temperature, initial grain size, and post-deformation temperature. Notably, grain size tends to decrease with increasing strain magnitude, higher strain rates, lower temperatures, and smaller initial grain dimensions.

3.3 Grain Growth

The grain growth process is a critical phase in material microstructure evolution, directly determining the final grain size of materials. The mechanism involves grain boundary energies in the microstructure becoming unstable under specific temperature conditions. To reduce local energy and achieve structural stability, grain boundaries undergo migration and coalescence, thereby decreasing their total surface area. This leads to grain enlargement, shrinkage, and fusion processes, collectively manifesting as grain growth behavior. According to our research team's findings, Figure 8 illustrates the grain size variation trends of forged GH4169 alloy after different holding times at varying temperatures.

The grain growth process occurs throughout all thermal deformation stages of materials, including the hot state during forging, the deformation process itself, and the post-deformation phase when materials remain at elevated temperatures. Grain growth is primarily influenced by temperature, solid solution elements, second-phase particles, and microstructure, with temperature being the most critical factor. Temperature significantly impacts grain growth by modulating the driving force and velocity of grain boundary migration, with elevated temperatures markedly accelerating the growth process. Solid solution elements and second-phase particles exert their effects through pinning mechanisms that impede grain boundary migration, where specific impacts depend on their concentration, type, size, and distribution, resulting in complex interactions. If the driving force for grain boundary migration fails to overcome pinning effects, grain growth proceeds slowly until reaching a stable size. The pinning mechanism induces grain boundary redistribution and precipitation processes, making second-phase particles crucial for grain growth dynamics. As these particles undergo consumption and Ostwald maturation during growth, pinning effects weaken. Conversely, sudden increases in driving forces that exceed pinning resistance lead to rapid grain growth—a phenomenon known as austenite grain coarsening. Microstructural factors also hinder grain growth, as materials with complex microstructures contain more low-energy small-angle grain boundaries (subgrain boundaries), which amplify the required driving force for grain growth.

4Analysis of Penetrability in Radial Forging Process

The depth of plastic deformation achievable in the longitudinal cross-section of a forging blank during forging is referred to as forgeability. To quantify forgeability, a standard has been established: if the equivalent strain value in the core of the blank exceeds 0.2, it is deemed fully forgeable (i.e., forgeability reaches 100%). As cast materials typically contain defects such as internal voids, porosity, and inclusions, products manufactured from them often fail to meet mechanical performance requirements. Radial forging blanking eliminates defects like porosity and shrinkage cavities formed during metal melting while improving microstructural organization. Since radial forging blanking preserves metal flow lines more intact, the resulting material generally exhibits superior mechanical properties compared to cast materials, yielding products with enhanced durability and longer service life. The deformation of grain structures, coupled with dynamic recrystallization and grain growth under thermal activation conditions, constitutes the fundamental process of ingot blanking. Through recrystallization, ingots develop fine-grained structures, producing blanks with excellent machinability that facilitates subsequent processing operations.

4.1 Empirical Triangle Method

The Germans were the first to propose the concept of forging penetration for GFM precision forging machines based on classical theory. This concept defines the depth of penetration by measuring the contact length between the hammer head and the workpiece, which forms an isosceles right triangle (Figure 9). In Figure 9, D represents the original diameter of the workpiece; A, B, and C are the vertices of the isosceles right triangle, with AC indicating the contact length between the hammer head and workpiece during forging (serving as the base side of the triangle). According to GFM classical theory, constructing an isosceles right triangle with AC as the base side determines that the depth at vertex B represents the maximum forging penetration depth under given conditions.

Where: E is the forging through depth (mm); h is the single-side penetration (mm); α is the angle between the hammer head inclined surface and the blank (°).

In subsequent research, Xu Fang and colleagues extended the triangular rule originally developed for predicting forging penetrability of cylindrical billets during radial forging processes to rectangular-section components, making corresponding modifications and proposing a novel forging penetrability calculation model. Building upon empirical triangular formulas, Luan Qiancong and his team derived a new equation for calculating forging penetrability (Equation 2). Using MSC.Marc/Mentat finite element software, they conducted in-depth investigations into radial forging penetrability from the perspectives of equivalent plastic strain and axial stress distribution.

Where: ηfg denotes the forging penetration rate; ηz represents the feed rate; ηrs indicates the radius ratio; and β is the acute angle between the hammer head's inclined surface and the billet.

4.2 Analytical Method

In the 1970s, Lahoti and Altan employed the principal stress method to develop an axisymmetric model for analyzing radial forging processes of pipes. By setting the inner diameter of pipes to zero, this model was extended to radial forging analysis of solid bars. Figure 10 illustrates the three distinct deformation zones during radial forging: the sinking zone, forging zone, and sizing zone, with simplified mechanical equilibrium equations established for each region. Assuming the flow separation surface lies within the forging zone, the opposing axial flow directions of metals on both sides generate counteracting friction forces, resulting in distinct radial compressive stress distributions on either side of the separation plane. Based on the continuity of radial compressive stress at separation points, a nonlinear algebraic equation with separation surface position as an unknown variable was formulated. Solving this equation revealed correlations between radial compressive stress distribution and process parameters (e.g., radial reduction amount, axial feed rate, friction factor) as well as hammer structure parameters (e.g., cone angle, sizing zone length). Integrating compressive stress values across regions enables accurate calculation of radial loads.

Yang proposed a numerical method that integrates slip line field theory with upper bound theorems, employing nonlinear optimization techniques for computational analysis. The study investigated stress field distribution, root crack formation mechanisms, and internal forging penetration conditions of workpieces, introducing the concept of forging permeability and determining optimal process parameters accordingly. Wang Zhenfan et al. applied the flow function method to analyze forging permeability in GFM materials, quantifying the influence of feed rate, hammer dimensions, and geometry through flow function analysis. The dense grid cloud pattern method (abbreviated as cloud pattern method) is an experimental analytical technique. Its principle involves attaching a sample grid to the specimen during deformation, followed by overlaying it with a reference grid. Stress-strain states at deformation initiation are determined by analyzing overlapping cloud patterns combined with plasticity theory.

4.3 Finite Element Analysis Method

With advancements in computer technology, finite element analysis techniques have been widely adopted in industrial applications. In radial forging research, scholars worldwide predominantly employ numerical simulation methods to investigate the distribution patterns of stress, strain/strain rate, temperature, and other field variables under varying processing conditions. Based on analytical dimensions, existing radial forging finite element models can be categorized into two main types: axisymmetric models and three-dimensional models. By neglecting billet rotation and clearance between adjacent hammer heads, the radial forging process can be simplified into an axisymmetric model, significantly reducing simulation complexity. During radial forging operations, it is essential to establish stress-strain constitutive models and grain structure evolution models to analyze material behavior during forging processes.

4.3.1 Material Stress-Strain Constitutive Model

To simulate forging processes and grain evolution during these processes, it is first necessary to establish a stress-strain constitutive model for materials under deformation. Subsequently, a finite element model for working formation processes is developed and computed. By integrating grain evolution patterns during material deformation, a grain model for forging processes is constructed to achieve accurate simulation of working formation processes and their microstructural outcomes.

The constitutive models of materials currently employed in research can be broadly categorized into three types: phenomenological models, physics-based models, and artificial neural network models. Phenomenological models have gained the most widespread application. Typical examples include the Johnson-Cook model, Arrhenius model, Fields-Backofen model, and neural network models. The Arrhenius model incorporates factors such as temperature and strain rate affecting material rheological stress, and is widely applied in forging process simulations based on deformation activation energy theory. By considering the relationship between temperature, strain rate, and material rheological stress, the Arrhenius constitutive model proves particularly suitable for high-temperature conditions in thermal deformation studies, making it the most widely adopted model. Its typical formulations are illustrated in Equations (3) to (5).

Here, σ denotes stress, n is the stress exponent derived from experimental data fitting, and Z represents the Zener-Hollomon parameter proposed by Zener and Hollomon in 1944, which forms the basis of the Arrhenius constitutive model. Its influence terms include strain rate ε, deformation activation energy Qdef, temperature T, and R (gas constant). The parameters A, α, β, and Qdef in the equation are obtained through fitting, with α = β/n. Two expressions of the resulting equation are presented in Equations (6) to (7).

The fundamental Arrhenius equation fails to account for the influence of strain rate on material rheological stress, which constitutes its primary limitation. To address this deficiency, Lin et al. incorporated parameters such as Q, n, and lnA from the Arrhenius equation into a fifth-order polynomial function of strain. This modified Arrhenius equation demonstrates applicability for rheological stress simulation under various deformation conditions while maintaining high accuracy. Physically meaningful material constitutive models are developed based on the physical principles underlying actual processes, systematically elucidating the stress-strain characteristics of materials. The advantage of such models lies in their theoretical foundation, enabling clear interpretation of computational processes and results. However, their theoretical framework often presents complexity and inherent limitations, making it challenging to achieve precise alignment with experimental observations.

Typical flow stress models based on physical principles include the Lin et al. model, ZA model, and PTW model. Notably, the Lin et al. model specifically considers the effects of dynamic recovery and dynamic recrystallization on material rheological stress during thermal deformation processes. In constructing the initial plasticity model, the entire deformation process is divided into four distinct stages: work hardening stage, transition stage, softening stage, and steady-state stage. By integrating mechanisms across these stages, the rheological stress of materials is calculated, ultimately yielding constitutive equations for scenarios involving either dynamic recovery alone or simultaneous dynamic recovery and dynamic recrystallization, as illustrated in Formulas (8) and (9). Under conditions of isolated dynamic recovery, Equation (8) defines σ0 as the material's yield stress, σDRV as the final steady-state rheological stress achieved during softening processes with only dynamic recovery (typically obtained through extrapolation methods), and Ω as the coefficient representing softening effects in strain-dependent dislocation density evolution equations. For simultaneous dynamic recovery and recrystallization, Equation (9) introduces parameters Kd and nd requiring fitting; σp denotes peak stress, σDRX represents the final steady-state flow stress under dynamic recrystallization conditions, and εc indicates the critical strain threshold for dynamic recrystallization.

4.3.2 Grain Structure Evolution Model

To achieve accurate prediction and control of forging process microstructure, precise and reliable simulation of grain structure evolution during forging is essential. The forging process may involve various mechanisms including grain growth, work hardening and recovery, dynamic recrystallization, subdynamic recrystallization, and static recrystallization. These processes can all lead to microstructural changes. Subdynamic recrystallization, however, has not been considered due to the technical challenges in separate analysis compared to dynamic recrystallization. Static recrystallization occurs over short durations (typically several seconds) and is generally regarded as having negligible impact compared to dynamic recrystallization. Grain growth, work hardening and recovery, and dynamic recrystallization represent the three primary mechanisms requiring attention during forging processes.

The classical equation for grain growth was proposed by Sellars et al. in 1979 during their study on recrystallization and grain growth in hot rolling processes. Experimental results demonstrated that grain size changes during grain growth are correlated with initial grain size (d0), time (t), activation energy (Qgg), and temperature (T). The derived equation is presented in Equation (10).

Where m and C represent material influence factors. As a typical macroscopic model for grain growth processes, this model has been widely applied and studied.

The classical model for work hardening and recovery processes was proposed by Mecking and Kocks. This model can be divided into two main components: one describing the relationship between rheological stress and dislocation density, and the other describing the temporal evolution of dislocation density. For the model of the relationship between rheological stress and dislocation density, the model typically presented in Equation (11) is commonly used.

Here, σ denotes the rheological stress, α represents the initial rheological stress of the material at zero dislocation density, μ is the material's shear modulus, b is the Birkhoff vector, and ρ is the material constant.

Dynamic recrystallization models can be broadly categorized into two types: macroscopic models and microscopic models. Macroscopic models primarily rely on experimental data, accounting for factors such as temperature, strain rate, strain, and initial grain size during thermal deformation processes. These models propose empirical equations and obtain relevant parameters through fitting methods to simulate dynamic recrystallization processes. The most widely used model currently is the Johnson-Mehl-Avrami-Kolmogorov (JMAK) model. Originally developed for static recrystallization scenarios, this model has been successfully applied to dynamic recrystallization studies, achieving high accuracy in simulating recrystallization ratios and steady-state grain sizes. The JMAK model incorporates influences from temperature, strain rate, strain, and initial grain size on dynamic recrystallization processes. Its equations consist of two components: recrystallization ratio simulation and dynamic grain size simulation, with typical models illustrated by Equations (12) and (13).

Among them, XDRX represents the rate of dynamic recrystallization; Kd and βd are fitting parameters; εc denotes the critical strain required for dynamic recrystallization, while ε0.5 is the strain at which the dynamic recrystallization rate reaches 50%. These two variables are typically expressed in the form of Equation (14) during processing.

d0 denotes the initial grain size; ε represents the strain rate; ε indicates the strain; dDRX stands for dynamic recrystallization grain size; while the indices l, m, and n are parameters derived from experimental fitting. The JMAK model demonstrates high simulation accuracy for dynamic recrystallization processes, though its primary limitation lies in the relatively weak physical interpretation.

Microscopic models are developed based on the physical principles of dynamic recrystallization processes. In model equation formulation, discontinuous dynamic recrystallization processes are typically divided into four distinct phases: work hardening, recovery, nucleation, and growth. Corresponding model equations are established for each phase, with integrated solutions derived to characterize grain structure evolution. While the modeling approaches for grain structure evolution differ little across various microscopic models, their solution methodologies exhibit significant variations.

Current numerical simulation software commonly used in forging processes primarily includes Deform, Abaqus, Marc, and Ansys. Among these, Deform is specifically designed for forging process simulation, featuring robust tetrahedral mesh generation capabilities and mesh refinement functions, making it particularly suitable for large-deformation processes like forging. Its application in forging simulations offers advantages such as powerful functionality and user-friendly interfaces. Abaqus, Marc, and Ansys are comprehensive finite element software solutions with broad applicability. As general-purpose tools, they employ superior solution algorithms and can effectively simulate forging processes when appropriately configured. In practice, all four simulation software packages mentioned above are applicable to forging process modeling. Through secondary development and input of material constitutive models along with grain structure evolution models, they can accurately simulate stress-strain variations and grain structure changes during ring forging processes.

Compared to traditional analytical methods, the finite element method (FEM) demonstrates superior capability in addressing complex problems while delivering more accurate and detailed post-processing results. However, radial forging processes involve substantial computational demands, resulting in lower efficiency for multi-pass full-process simulations. Furthermore, as FEM simulation constitutes a forward analysis approach that evaluates performance metrics based on known process parameters, radial forging process design presents a reverse engineering challenge. This requires identifying optimal solutions within an unknown parameter space while adhering to predefined performance constraints. Consequently, FEM models cannot be directly applied to radial forging process design. Instead, computational results from FEM simulations must first be utilized to construct surrogate models through techniques such as response surface methodology and artificial neural networks. These surrogate models subsequently serve as objective functions for optimization algorithms, enabling subsequent process design improvements.

5Summary and Outlook

As critical materials for high-temperature components in aero-engine systems, superalloys play an indispensable role in national development and are classified as highly important materials. However, controlling the microstructure of superalloys remains challenging in practical production. Radial forging, as an efficient and advanced metal forming technology, demonstrates exceptional performance in improving material microstructure, enhancing mechanical properties, and optimizing material utilization through its high-frequency pulse forging and multi-directional die forging characteristics. This paper reviews global advancements in radial forging technology, explores core technologies including forging equipment, processing techniques, microstructural evolution, and forgeability analysis, and analyzes the significant advantages of radial forging processes over traditional free forging methods in material processing. Additionally, it provides a concise overview of research methodologies for radial forging technology.

1) Technological Advances and Industrial Applications: Radial forging, as an advanced metal forming technology, demonstrates significant advantages in improving the microstructure, mechanical properties, and material utilization efficiency of high-temperature alloys. Although this technology has been widely applied domestically, most radial forging equipment still relies on imports, and domestic independent R&D efforts need to be strengthened to meet the growing demands across various fields.

2) Challenges in process optimization: The radial forging process involves complex phenomena such as recovery, work hardening, recrystallization, and grain growth. Existing empirical triangular methods and analytical approaches primarily rely on idealized assumptions, failing to adequately account for actual operating conditions and material properties. Although finite element analysis can provide relatively accurate simulations, further research is needed to develop physically meaningful models that better understand and control microstructural and property changes during forging processes.

3) Future Development Directions: To ensure continuous advancement in radial forging technology, close collaboration between academia and industry is essential. Priority should be given to strengthening theoretical research, promoting domestic R&D of radial forging equipment, and optimizing process parameters to enhance the performance of high-temperature alloys, thereby supporting the upgrading of China's manufacturing sector. Through ongoing technological innovation and industrialization efforts, radial forging technology will play a pivotal role in producing high-performance alloys, reducing production costs, and meeting advanced manufacturing demands. This will facilitate the transformation and upgrading of China's manufacturing industry while boosting its global competitiveness.